Question: Question: Consider the one-variable regression model Yj = AYO + AYIXi + ui, and suppose that it satisfies the assumption in Key Concept 4.3. Suppose

Question: Consider the one-variable regression model Yj = AYO + AYIXi + ui, and suppose that it satisfies the assumption in Key Concept 4.3. Suppose that Yi is measured with error, so the data are y, = Y + wi. A where wi is the measurement error which is i.i.d. and independent of Yi and Xi. Consider the population regression = + gx+ A where vi is the regression error usingA the mismeasured dependent variable, pi a. Show that vi = ui + wi. b. Show that the regression y - Bo + B,X, + >, A satisfies the assumptionsA in Key Concept 4.3. (Assume that wi is independent of Yj and Xj forA all values of i and j and has a finite fourth moment.) c. Are the OLS estimators consistent? d. Can confidence intervals be constructed in the usual way? e. Evaluate these statements: afoeMeasurement error in the XaCTMs is a seriousA problem. Measurement error in Y is not.aft

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